The model presented in Section  can be extended by adding the cost to update the cache state after the batch of \(R\)  requests has been served. This cost may quantify the additional load on the server or on the network. This update cost is often called a movement cost [1]} or switching cost [2]}.
As the state changes from \(\mathbf {x}_t\)  to \(\mathbf {x}_{t+1}\) , the cache evicts part of the file \(i\)  if \(x_{t+1,i} < x_{t,i}\)  and stores additional bytes of it if \(x_{t+1,i} > x_{t,i}\) .
We make the following assumptions:
